Area of parallelogram

Question

PQRS is a rectangle in which PQ=7 cm and QR= 16 cm. PT:TS=5:3. Find the areas of the quadrilateral TQRS and triangle PQT

Answer 1

 

 

 

Imagine a Rectangle PQRS and quadrilateral TQRS where T lies on side PS which is parallel to QR = 16

 

If PT is x, then TS = 16-x

 

The ratio PT/TS = 5/3

 

Substituting the sides by x and 16-x , we get:

 

x/(16-x) = 5/3

 

solving for x by cross multiplying, we get:

 

3x = 5(16-x)

 

x= 10 = PT

16-x = 16-10 = 6 = TS

 

From here the area of the triangle PQT = (1/2)*7*10 =35

The area of the rectangle inside is 6*7 = 42

Area of TQRS = 35+42 = 77

 

If you draw the figure accordingly, you can get the picture.

 

 

Answer 2

Hi Sam,

 

In order to form triangle PQT and quadrilateral TQRS, point T must lie on line PS which is 16 cm. long.

 

If the ratio of PT to TS is 5:3 and the total length of PS is 16, then PT must be 10 and TS must be 6 (10 + 6 =16) and 10:6 is the same ratio as 5:3.  Another way to think about it is 5/3 = 10/6.

 

Now you have all the lengths that you need to find the areas of the quadrilateral and the triangle.

 

Make sure you draw a diagram of it!!

 

Have fun.

 

Dan